Priming Mindfulness Project

Comparison & analysis report

Introduction

This report describes the results of the first priming mindfulness study. It was initially made using Dominique Makowski’s Supplementary Materials template. Two similar templates will be created based on the two online pilot studies from the Varela project.

This is an exploratory (not confirmatory) study. The result of this exploration will be used to conduct a second, confirmatory, preregistered study.

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Note also that this data has been cleaned beforehand. Five datasets were merged (joined) through a full join—3 Qualtrics surveys and 2 Inquisit tasks—so as to keep as much data as possible. Missing data resulting from this full join will be imputed later on. Duplicates were addressed with the rempsyc::best_duplicate function, which keeps the duplicate with the least amount of missing values, and in case of ties, takes the first occurrence.

Packages & Data

Packages

library(rempsyc)
library(dplyr)
library(interactions)
library(performance)
library(see)
library(ggplot2)
library(report)
library(bestNormalize)
library(psych)
library(visdat)
library(missForest)
library(doParallel)

summary(report(sessionInfo()))

The analysis was done using the R Statistical language (v4.2.1; R Core Team, 2022) on Windows 10 x64, using the packages iterators (v1.0.14), doParallel (v1.0.17), interactions (v1.1.5), performance (v0.9.2.2), see (v0.7.1), report (v0.5.5.1), foreach (v1.5.2), bestNormalize (v1.8.3), psych (v2.2.5), missForest (v1.5), rempsyc (v0.0.9), visdat (v0.5.3), ggplot2 (v3.3.6) and dplyr (v1.0.9).

Data

# Read data
data <- read.table("data/fulldataset.txt", sep = "\t", header = TRUE)

# Dummy-code group variable
data <- data %>% 
  mutate(condition_dum = ifelse(condition == "Mindfulness", 1, 0),
         condition = as.factor(condition))

cat(report_participants(data, threshold = 1))

585 participants (Country: 90.60% USA, 2.56% missing, 2.22% India, 1.54% Canada, 1.20% Kenya, 1.88% other)

# Allocation ratio
report(data$condition)

x: 2 levels, namely Control (n = 181, 30.94%), Mindfulness (n = 178, 30.43%) and missing (n = 226, 38.63%)

Taylor Task…

In this stage, we define a list of our relevant variables and standardize them according to the Median Absolute Deviation (MAD), which is more robust to extreme observations than standardization around the mean.

Preparation

# Make list of DVs
col.list <- c("blastintensity", "blastduration", "blastintensity.duration",
              "blastintensity.first", "blastduration.first", 
              "blastintensity.duration.first", "all50trials", "KIMS", 
              "BSCS", "BAQ", "SOPT", "IAT")

# Create new variable blastintensity.duration
data <- data %>% 
  mutate(blastintensity.duration = blastintensity * blastduration,
         blastintensity.duration.first = 
           blastintensity.first * blastduration.first,
         .after = blastduration)

Blast Intensity * Duration

Why combine the intensity and duration scores? Should we? For a discussion, see:

Elson, M., Mohseni, M. R., Breuer, J., Scharkow, M., & Quandt, T. (2014). Press CRTT to measure aggressive behavior: the unstandardized use of the competitive reaction time task in aggression research. Psychological assessment, 26(2), 419. https://doi.org/10.1037/a0035569

• Bushman and Baumeister (1998) used the sum of volume and duration settings in the first of 25 trials [p. 3]
• Lindsay and Anderson (2000) multiplied volume with log-transformed duration settings. The average over 25 trials of those products was their measure for overall aggression.
• Carnagey and Anderson (2005) averaged the products of volume and the square root of duration to form a single “aggressive energy score” (p. 887). No reason is given for this other than the claim that this single score supposedly is a valid measure and that duration should be square rooted.
• Bartholow, Sestir, and Davis (2005) multiplied the average volume and duration settings to form a composite aggressive behavior score. Although Bartholow, Bushman, and Sestir (2006) also used volume and duration settings, they standardized and summed the two parameters instead of multiplying them.
• Sometimes the option of setting the volume and/or duration to zero as a way to act nonaggressively is provided. Including settings of zero as an option also raises further questions, for example, how to handle trials in which participants set only one of the two intensity parameters to zero. [Note: we do have zero as option]
• With regard to the analysis, there is no definitive answer to the question of how to calculate aggression scores, or whether different scores might measure different types of aggression, as long as none of them have been properly validated. As it seems that volume and duration do not measure the exact same construct, it is advisable to consider them as separate measures for related subdimensions of aggression.

First sound blast

Why use the first sound blast only instead of the average of all trials? Should we?

According to some, the Taylor Aggression Paradigm is not a measure of aggression per say, but of reactive aggression, because participants react to the other “participant’s” aggression. They suggest that for a pure measure of aggression, it is recommended to use only the first sound blast used by the participant before he receives one himself. At this stage, we attempt the analyses with all these different measures of aggression for exploratory purposes. See earlier reference to Elson et al. (2014):

• If researchers are interested in measuring unprovoked aggression, they should also look at the settings in the first trial. Those studying provoked aggression or retaliation, on the other hand, should focus on all trials except the first one.

Problems in measurement

We note that Lobbestael et al. (2021) suggests, based on factor analysis, separately averaging all preprovocation versus all postprovocation trials. However, this recommendation applies to the 30-trial version (we have the 25 trial version). They add:

• In contrast to the 30-trial version, the 25-trial CRTT version showed to be underlined by one single factor, clustering the duration and volume of both provoked and unprovoked trials, irrespective of whether these were preceded by win or lose experiences.

Lobbestael, J., Emmerling, F., Brugman, S., Broers, N., Sack, A. T., Schuhmann, T., … & Arntz, A. (2021). Toward a more valid assessment of behavioral aggression: An open source platform and an empirically derived scoring method for using the Competitive Reaction Time Task (CRTT). Assessment, 28(4), 1065-1079. https://doi.org/10.1177/1073191120959757

Therefore, it is assumed safe to use and combine all 25 trials. However, we also note (again) the very high heterogeneity in quantification strategies:

• Why the Flexibility is Problematic There are currently 130 publications in which results are based on the CRTT, and they reported 157 different quantification strategies in total! Given the number of different versions of the CRTT measure that can be extracted from its use in a study, it is very easy for a researcher to analyze several (or several dozen) versions of the CRTT outcome measures in a study, running hypothesis tests with one version of the measure after another until a version is found that produces the desired pattern of results. Given that the measure has been used in several dozen different ways in the published research, and often in multiple ways by the same authors (and sometimes even in multiple ways for different analyses within the same paper), it appears likely that selective reporting of results after exploring analyses with multiple versions of the CRTT is not uncommon. Even if multiple quantifications used are reported in a paper, it is often not clear how to interpret the findings given that in many cases one quantification strategy does not have greater validity than others.

See: https://www.flexiblemeasures.com/crtt/

Thus the recommandations are:

1. Preregistration of Analysis Plan
2. Preregistration of Decision Tree (e.g., regarding data transformation)
3. Defense of Selected Quantification Strategy

See: https://www.flexiblemeasures.com/crtt/index.php?menu=recommendations

Average of all 50 trials

After discussion with Dr. David Chester, it was also suggested to use the average of all 50 standardized trials, as in Chester & Lasko 2019 and Lasko & Chester (2022).

Chester & Lasko (2019). Validating a standardized approach to the Taylor Aggression Paradigm. Social Psychological and Personality Science, 10(5), 620-631. https://doi.org/10.1177/1948550618775408

Lasko & Chester (2022). Measurement invariance and item response theory analysis of the taylor aggression paradigm. Assessment, 29(5), 981-992. https://doi.org/10.1177/1073191121996450

Still, he also notes,

In one of our papers, we show that the major approaches to scoring the CRTT typically arrive at the same result, so in the end, the scoring strategy you choose is unlikely to have a large effect on your findings.

That said, technically speaking, if a participant sets the intensity to 10, but duration to 0, there is no actual sound blast for that trial. Similarly, if a participant sets the duration to 10, but intensity to 0, there is no actual sound blast for that trial. Taking the product of intensity and duration takes this dynamic into account. In contrast, other methods using the sum of intensity and duration, or yet again the average of all 50 trials (intensity and duration) does not. That said, perhaps it is not a big deal given that this particular scenario (including 0 for one of the two settings) is probably rare.

Edit: Following another discussion, Dr. Chester pointed out that it is possible to measure how often this scenario of mismatching zero intensity occurs. Let’s test this right here.

# Blastintensity = 0
data %>% 
  filter(blastintensity == 0) %>% 
  summarize(percent = round(sum(blastduration !=0)/nrow(data) * 100, 2))

percent
0.34

# Blastduration = 0
data %>% 
  filter(blastduration == 0) %>% 
  summarize(percent = round(sum(blastintensity !=0)/nrow(data) * 100, 2))

percent
0

So we have 0.37% and 0% of the data in this scenario, respectively.

Dr. Chester also recommends a better (but more complex) approach:

If it’s possible, a superior approach to this aggregate scoring strategy is to employ multilevel modeling instead of a univariate analysis. When you aggregate across all 50 of the individual CRTT measures, you are losing a lot of information/variability/statistical-power. Multilevel modeling on the non-aggregated data allows you to retain this variability.

Although it is not clear so far if this technique can be applied to our particular situation. Further study will be required.

Data cleaning

In this section, we are preparing the data for analysis: (a) taking care of preliminary exclusions, (b) checking for and exploring missing values, (d) imputing missing data with missForest, (e) computing scale means, and (f) extracting reliability indices for our scales.

Preliminary exclusions

First, we only want to keep those who agreed to keep their participation in the study after the debriefing.

data %>% 
  filter(debrief.consent != 1 | is.na(debrief.consent)) %>% 
    nrow

## [1] 300

There’s 300 people that would be excluded. That’s a lot, but this is what we’ve got.

data <- data %>%
    filter(debrief.consent == 1)
cat(report_participants(data, threshold = 1))

285 participants (Country: 94.04% USA, 1.40% Canada, 1.40% India, 1.40% missing, 1.75% other)

Second, we know that we only want to keep participants who had at least an 80% success rate in the critical experimental manipulation task. Let’s see how many participants have less than an 80% success rate. Those with missing values for variable manipsuccessleft will also be excluded since they have not completed the critical experimental manipulation in this study.

data %>% 
    summarize(success.80 = sum(manipsuccessleft < .80, na.rm = TRUE),
              is.na = sum(is.na(manipsuccessleft)))

success.80	is.na
18	0

There’s 18 people with success smaller than 80%, let’s exclude them.

data <- data %>% 
    filter(manipsuccessleft >= .80)
cat(report_participants(data, threshold = 1))

267 participants (Country: 95.13% USA, 1.50% missing, 1.12% Canada, 2.25% other)

Explore missing data

Missing items

# Check for nice_na
nice_na(data, scales = c("BSCS", "BAQ", "KIMS"))

var	items	na	cells	na_percent	na_max	na_max_percent	all_na
BSCS_1:BSCS_7	7	0	1869	0.00	0	0.00	0
BAQ_1:BAQ_12	12	0	3204	0.00	0	0.00	0
KIMS_1:KIMS_39	39	0	10413	0.00	0	0.00	0
Total	156	162	41652	0.39	88	56.41	0

Patterns of missing data

Let’s check for patterns of missing data.

# Smaller subset of data for easier inspection
data %>%
  select(manualworkerId:BAQ_12, IAT, SOPT, 
         condition, manipsuccessleft,
         blastintensity.first:blastduration.first,
         blastintensity, blastduration,
         blastintensity.duration:blastintensity.duration.first,
         KIMS_1:KIMS_38) %>%
  vis_miss

Little’s MCAR test

# Let's use Little's MCAR test to confirm
# We have to proceed by "scale" because the function can only
# support 30 variables max at a time
library(naniar)
data %>% 
  select(BSCS_1:BSCS_7) %>% 
  mcar_test

statistic	df	p.value	missing.patterns
0	0	0	1

data %>% 
  select(IAT_values.completed:IAT) %>% 
  mcar_test

statistic	df	p.value	missing.patterns
179.3354	2	0	2

data %>%
 select(taylor_values.completed:taylor_expressions.meanrt_target) %>%
 mcar_test

statistic	df	p.value	missing.patterns
0	0	0	2

data %>%
 select(taylor_values.blastduration_9:taylor_values.blastintensity_9) %>%
 mcar_test

statistic	df	p.value	missing.patterns
0	0	0	2

data %>%
 select(taylor_values.blastintensity_18:taylor_values.blastintensity_225) %>%
 mcar_test

statistic	df	p.value	missing.patterns
0	0	0	2

data %>% 
  select(KIMS_1:KIMS_39) %>% 
  mcar_test

statistic	df	p.value	missing.patterns
0	0	0	1

Impute missing data

…

Here, we impute missing data with the missForest package, as it is one of the best imputation methods.

Details

missForest outperforms other imputation methods, including the popular MICE (multiple imputation by chained equations). You also don’t end up with several datasets, which makes it easier for following analyses. Finally, it can be applied to mixed data types (missings in numeric & categorical variables).

Waljee, A. K., Mukherjee, A., Singal, A. G., Zhang, Y., Warren, J., Balis, U., … & Higgins, P. D. (2013). Comparison of imputation methods for missing laboratory data in medicine. BMJ open, 3(8), e002847. https://doi.org/10.1093/bioinformatics/btr597

Stekhoven, D. J., & Bühlmann, P. (2012). MissForest—non-parametric missing value imputation for mixed-type data. Bioinformatics, 28(1), 112-118. https://doi.org/10.1093/bioinformatics/btr597

# Need character variables as factors
# "Error: Can not handle categorical predictors with more than 53 categories."
# So we have to temporarily remove IDs also...
new.data <- data %>% 
  select(-c(manualworkerId, embeddedworkerId)) %>% 
  mutate(across(where(is.character), as.factor))

# Parallel processing
registerDoParallel(cores = 4)

# Variables
set.seed(100)
data.imp <- missForest(new.data, verbose = TRUE, parallelize = "variables")

##   parallelizing over the variables of the input data matrix 'xmis'
##   missForest iteration 1 in progress...done!
##     estimated error(s): 0.4843203 0.01711027 
##     difference(s): 0.00003537224 0 
##     time: 13.26 seconds
## 
##   missForest iteration 2 in progress...done!
##     estimated error(s): 0.4853189 0.01711027 
##     difference(s): 0.00001395253 0 
##     time: 11.91 seconds
## 
##   missForest iteration 3 in progress...done!
##     estimated error(s): 0.4759759 0.01711027 
##     difference(s): 0.00003754515 0 
##     time: 9.69 seconds

# Total time is 42 sec (3*14) - 4 cores

# Extract imputed dataset
new.data <- data.imp$ximp

There are some variables we don’t actually want to impute, like country. We want to keep those NAs in that case. Let’s add them back. We also want to add ID back.

# Add ID
new.data <- bind_cols(manualworkerId = data$manualworkerId, new.data)

# Add back the NAs in country
new.data <- new.data %>% 
  mutate(country = data$country)

Scale Means

…

Now that we have imputed the missing data, we are ready to calculate our scale means.

Self-control

# Reverse code items 2, 4, 6, 7
new.data <- new.data %>% 
  mutate(across(starts_with("BSCS"), .names = "{col}r"))
new.data <- new.data %>% 
  mutate(across(c(BSCS_2, BSCS_4, BSCS_6, BSCS_7), ~nice_reverse(.x, 5), .names = "{col}r"))

# Get mean BSCS
new.data <- new.data %>% 
  mutate(BSCS = rowMeans(select(., BSCS_1r:BSCS_7r)))

Trait aggression

# Reverse code item 7
new.data <- new.data %>% 
  mutate(across(starts_with("BAQ"), .names = "{col}r"))
new.data <- new.data %>% 
  mutate(across(BAQ_7, ~nice_reverse(.x, 7), .names = "{col}r"))

# Get sum of BAQ
new.data <- new.data %>% 
  mutate(BAQ = rowMeans(select(., BAQ_1r:BAQ_12r)))

Trait Mindfulness

# Reverse code items 3-4, 8, 11-12, 14, 16, 18, 20, 22, 23-24, 27-28, 31-32, 35-36
new.data <- new.data %>% 
  mutate(across(starts_with("KIMS"), .names = "{col}r"))
new.data <- new.data %>% 
  mutate(across(all_of(paste0("KIMS_", c(3:4, 8, 11:12, 14, 16, 18, 20,
                                         22:24, 27:28, 31:32, 35:36))), 
                ~nice_reverse(.x, 5), .names = "{col}r"))

# Get sum of KIMS
new.data <- new.data %>% 
  mutate(KIMS = rowMeans(select(., KIMS_1r:KIMS_39r)))

Reliability

…

Now that we have reversed our items, we can get the alphas for our different scales.

Self-control

x <- new.data %>% 
  select(BSCS_1r:BSCS_7r) %>% 
  alpha
x$feldt

## 
##    95% confidence boundaries (Feldt)
##  lower alpha upper
##    0.8  0.83  0.86

Trait aggression

x <- new.data %>% 
  select(BAQ_1r:BAQ_12r) %>% 
  alpha
x$feldt

## 
##    95% confidence boundaries (Feldt)
##  lower alpha upper
##   0.78  0.81  0.84

Trait Mindfulness

x <- new.data %>% 
  select(KIMS_1r:KIMS_39r) %>% 
  alpha

## Warning in alpha(.): Some items were negatively correlated with the total scale and probably 
## should be reversed.  
## To do this, run the function again with the 'check.keys=TRUE' option

## Some items ( KIMS_17r KIMS_19r ) were negatively correlated with the total scale and 
## probably should be reversed.  
## To do this, run the function again with the 'check.keys=TRUE' option

x$feldt

## 
##    95% confidence boundaries (Feldt)
##  lower alpha upper
##   0.87  0.89   0.9

We are getting the “Some items ( KIMS_17r KIMS_19r ) were negatively correlated with the total scale and probably should be reversed.” warning. Let’s check these items. In the raw data, item 17 is:

17. “I notice how foods and drinks affect my thoughts, bodily sensations, and emotions.”

And item 19 is:

19. “When I do things, I get totally wrapped up in them and don’t think about anything else.”

Which corresponds to items 17 and 19 as described in the original paper (Baer, Smith, & Allen in 2004). They also make sense to not reverse-score, theoretically speaking; they seem to relate to mindfulness, not its absence. So it is kind of strange that psych::alpha is suggesting to reverse-score these items. Perhaps the scale is not meant to be used as a single factor since it contains four factor subscales.

Note: before the imputation, this warning was worse in the sense that a lot more items were flagged in this way: “Some items ( KIMS_1r KIMS_5r KIMS_9r KIMS_13r KIMS_17r KIMS_19r KIMS_21r KIMS_25r KIMS_33r KIMS_37r KIMS_38r ) were negatively correlated with the total scale and probably should be reversed.”

Taylor all trials

# Standardize and center all trials
new.data <- new.data %>%
  mutate(across(taylor_values.blastduration_9:taylor_values.blastintensity_225,
                ~(scale(.x) %>% as.vector),
                .names = "{col}_c"))

# Combine duration and intensity trials
new.data <- new.data %>%
  mutate(all50trials = rowMeans(select(
    ., taylor_values.blastduration_9_c:taylor_values.blastintensity_225_c), na.rm = TRUE)) #%>%
  #select(script.subjectid, all50trials)

hist(new.data$all50trials)

data <- new.data

t-tests

In this section, we will: (a) test assumptions of normality, (b) transform variables violating assumptions, (c) test assumptions of homoscedasticity, (d) identify and winsorize outliers, and (e) conduct the t-tests.

Normality

lapply(col.list, function(x) 
  nice_normality(data, 
                 variable = x, 
                 title = x,
                 group = "condition",
                 shapiro = TRUE,
                 histogram = TRUE))

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Several variables are clearly skewed. Let’s apply transformations. But first, let’s deal with the working memory task, SOPT (Self-Ordered Pointing Task). It is clearly problematic.

SOPT Exclusions

Let’s do an histogram proper to see if it helps diagnosing the problem with SOPT.

hist(data$SOPT)

That looks weird, there’s some obvious outliers here; they probably didn’t do the task correctly, especially since there’s a gap after 60 errors. Let’s see how many people made more than 60 errors.

data %>% 
  filter(SOPT > 60) %>% 
  count

n
11

There’s 10 people with more than 60 errors. Let’s exclude them.

data <- data %>% 
  filter(SOPT <= 60)
cat(report_participants(data, threshold = 1))

256 participants (Country: 94.92% USA, 1.56% missing, 1.17% Canada, 2.34% other)

Transformation

The function below transforms variables according to the best possible transformation (via the bestNormalize package), and also standardizes the variables.

predict_bestNormalize <- function(var) {
  x <- bestNormalize(var, standardize = FALSE, allow_orderNorm = FALSE)
  print(cur_column())
  print(x$chosen_transform)
  cat("\n")
  predict(x)
}

set.seed(100)
data <- data %>% 
  mutate(across(all_of(col.list), 
                predict_bestNormalize,
                .names = "{.col}.t"))

## [1] "blastintensity"
## I(x) Transformation with 256 nonmissing obs.
## 
## [1] "blastduration"
## I(x) Transformation with 256 nonmissing obs.
## 
## [1] "blastintensity.duration"
## Non-Standardized sqrt(x + a) Transformation with 256 nonmissing obs.:
##  Relevant statistics:
##  - a = 0 
##  - mean (before standardization) = 68.36266 
##  - sd (before standardization) = 32.6041 
## 
## [1] "blastintensity.first"
## I(x) Transformation with 256 nonmissing obs.
## 
## [1] "blastduration.first"
## I(x) Transformation with 256 nonmissing obs.
## 
## [1] "blastintensity.duration.first"
## Non-Standardized sqrt(x + a) Transformation with 256 nonmissing obs.:
##  Relevant statistics:
##  - a = 0 
##  - mean (before standardization) = 79.46114 
##  - sd (before standardization) = 45.27023 
## 
## [1] "all50trials"
## Non-Standardized asinh(x) Transformation with 256 nonmissing obs.:
##  Relevant statistics:
##  - mean (before standardization) = -0.00101692 
##  - sd (before standardization) = 0.628961 
## 
## [1] "KIMS"
## Non-Standardized Log_b(x + a) Transformation with 256 nonmissing obs.:
##  Relevant statistics:
##  - a = 0 
##  - b = 10 
##  - mean (before standardization) = 0.5313085 
##  - sd (before standardization) = 0.06093755 
## 
## [1] "BSCS"
## I(x) Transformation with 256 nonmissing obs.
## 
## [1] "BAQ"
## Non-Standardized sqrt(x + a) Transformation with 256 nonmissing obs.:
##  Relevant statistics:
##  - a = 0 
##  - mean (before standardization) = 1.728034 
##  - sd (before standardization) = 0.2775367 
## 
## [1] "SOPT"
## Non-Standardized Yeo-Johnson Transformation with 256 nonmissing obs.:
##  Estimated statistics:
##  - lambda = 0.2345109 
##  - mean (before standardization) = 3.456466 
##  - sd (before standardization) = 1.063851 
## 
## [1] "IAT"
## I(x) Transformation with 256 nonmissing obs.

col.list <- paste0(col.list, ".t")

Note. The I(x) transformations above are actually not transformations, but a shorthand function for passing the data “as is”. Suggesting the package estimated the various attempted transformations did not improve normality in those cases, so no transformation is used. This only appears when standardize is set to FALSE. When set to TRUE, for those variables, it is actually center_scale(x), suggesting that the data are only CENTERED because they need no transformation (no need to be scaled), only to be centered.

Let’s check if normality was corrected.

# Group normality
lapply(col.list, function(x) 
  nice_normality(data, 
                 x, 
                 "condition",
                 shapiro = TRUE,
                 title = x,
                 histogram = TRUE))

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Looks rather reasonable now, though not perfect (fortunately t-tests are quite robust against violations of normality).

We can now resume with the next step: checking variance.

Homoscedasticity

# Plotting variance
plots(lapply(col.list, function(x) {
  nice_varplot(data, x, group = "condition")
  }),
  n_columns = 3)

Variance looks good. No group has four times the variance of any other group. We can now resume with checking outliers.

Outliers

# Using boxplots
plots(lapply(col.list, function(x) {
  ggplot(data, aes(condition, !!sym(x))) + 
  geom_boxplot()
  }),
  n_columns = 3)

There are some outliers, but nothing unreasonable. Let’s still check with the 3 median absolute deviations (MAD) method.

find_mad(data, col.list, criteria = 3)

## 5 outlier(s) based on 3 median absolute deviations for variable(s): 
##  blastintensity.t, blastduration.t, blastintensity.duration.t, blastintensity.first.t, blastduration.first.t, blastintensity.duration.first.t, all50trials.t, KIMS.t, BSCS.t, BAQ.t, SOPT.t, IAT.t 
## 
## Outliers per variable: 
## 
## $SOPT.t
##   Row SOPT.t_mad
## 1  57  -3.499890
## 2 122   3.201579
## 3 146   3.252362
## 4 179  -3.499890
## 5 217   3.097682

There are 6 outliers after our transformations.

Winsorization

Visual assessment and the MAD method confirm we have some outlier values. We could ignore them but because they could have disproportionate influence on the models, one recommendation is to winsorize them by bringing the values at 3 SD. Instead of using the standard deviation around the mean, however, we use the absolute deviation around the median, as it is more robust to extreme observations. For a discussion, see:

Leys, C., Klein, O., Bernard, P., & Licata, L. (2013). Detecting outliers: Do not use standard deviation around the mean, use absolute deviation around the median. Journal of Experimental Social Psychology, 49(4), 764–766. https://doi.org/10.1016/j.jesp.2013.03.013

# Winsorize variables of interest with MAD
data <- data %>% 
  mutate(across(all_of(col.list), 
                winsorize_mad,
                .names = "{.col}.w"))

# Update col.list
col.list <- paste0(col.list, ".w")

Outliers are still present but were brought back within reasonable limits, where applicable.

Standardization

We can now standardize our variables.

data <- data %>%
  mutate(across(all_of(col.list),
                function(x) {
                  as.numeric(scale(x))
                  },
                .names = "{col}.s"))

# Update col.list
col.list <- paste0(col.list, ".s")

We are now ready to compare the group condition (Control vs. Mindfulness Priming) across our different variables with the t-tests.

t-tests

nice_t_test(data, 
            response = col.list, 
            group = "condition") %>% 
  nice_table(highlight = 0.10, width = .80)

## Using Welch t-test (base R's default; cf. https://doi.org/10.5334/irsp.82).
## For the Student t-test, use `var.equal = TRUE`. 
##  
## 

Interpretation: There is no clear group effect from our experimental condition on our different variables. There used to be a marginal effect on blastintensity, but it seems these have moved to the BAQ and IAT. But we know that the experimental manipulation could not have influenced these tasks, because they happen chronologically earlier. We still look at blastintensity visually for theoretical reasons and help choose the best measure.

Violin plots

Blast Intensity

nice_violin(data, 
            group = "condition", 
            response = "blastintensity.t.w.s",
            comp1 = 1,
            comp2 = 2,
            obs = TRUE,
            has.d = TRUE,
            d.y = 1)

Blast Duration

nice_violin(data, 
            group = "condition", 
            response = "blastduration.t.w.s",
            comp1 = 1,
            comp2 = 2,
            obs = TRUE,
            has.d = TRUE,
            d.y = 1)

Intensity * Duration

nice_violin(data, 
            group = "condition", 
            response = "blastintensity.duration.t.w.s",
            comp1 = 1,
            comp2 = 2,
            obs = TRUE,
            has.d = TRUE,
            d.y = 1)

1st Intensity

nice_violin(data, 
            group = "condition", 
            response = "blastintensity.first.t.w.s",
            comp1 = 1,
            comp2 = 2,
            obs = TRUE,
            has.d = TRUE,
            d.y = -0.8)

1st Duration

nice_violin(data, 
            group = "condition", 
            response = "blastduration.first.t.w.s",
            comp1 = 1,
            comp2 = 2,
            obs = TRUE,
            has.d = TRUE,
            d.y = -1.5)

1st Intensity * Duration

nice_violin(data, 
            group = "condition", 
            response = "blastintensity.duration.first.t.w.s",
            comp1 = 1,
            comp2 = 2,
            obs = TRUE,
            has.d = TRUE,
            d.y = -1.2)

50 trials

nice_violin(data, 
            group = "condition", 
            response = "all50trials.t.w.s",
            comp1 = 1,
            comp2 = 2,
            obs = TRUE,
            has.d = TRUE,
            d.y = 1)

Means, SD

Let’s extract the means and standard deviations for journal reporting.

Blast Intensity

data %>% 
    group_by(condition) %>% 
    summarize(M = mean(blastintensity),
              SD = sd(blastintensity),
              N = n()) %>% 
  nice_table(width = 0.40)

Blast Duration

data %>% 
    group_by(condition) %>% 
    summarize(M = mean(blastduration),
              SD = sd(blastduration),
              N = n()) %>% 
  nice_table(width = 0.40)

Intensity * Duration

data %>% 
    group_by(condition) %>% 
    summarize(M = mean(blastintensity.duration),
              SD = sd(blastintensity.duration),
              N = n()) %>% 
  nice_table(width = 0.40)

1st Intensity

data %>% 
    group_by(condition) %>% 
    summarize(M = mean(blastintensity.first),
              SD = sd(blastintensity.first),
              N = n()) %>% 
  nice_table(width = 0.40)

1st Duration

data %>% 
    group_by(condition) %>% 
    summarize(M = mean(blastduration.first),
              SD = sd(blastduration.first),
              N = n()) %>% 
  nice_table(width = 0.40)

1st Intensity * Duration

data %>% 
    group_by(condition) %>% 
    summarize(M = mean(blastintensity.duration.first),
              SD = sd(blastintensity.duration.first),
              N = n()) %>% 
  nice_table(width = 0.40)

50 trials

data %>% 
    group_by(condition) %>% 
    summarize(M = mean(all50trials),
              SD = sd(all50trials),
              N = n()) %>% 
  nice_table(width = 0.40)

Moderations

Let’s see if our variables don’t interact together with our experimental condition. But first, let’s test the models assumptions.

Assumptions

Blast Intensity

big.mod1 <- lm(blastintensity.t.w.s ~ condition_dum*KIMS.t.w.s + 
                 condition_dum*BSCS.t.w.s + condition_dum*BAQ.t.w.s + 
                 condition_dum*SOPT.t.w.s + condition_dum*IAT.t.w.s, 
               data = data, na.action="na.exclude")
check_model(big.mod1)

Blast Duration

big.mod2 <- lm(blastduration.t.w.s ~ condition_dum*KIMS.t.w.s + 
                 condition_dum*BSCS.t.w.s + condition_dum*BAQ.t.w.s + 
                 condition_dum*SOPT.t.w.s + condition_dum*IAT.t.w.s, 
               data = data, na.action="na.exclude")
check_model(big.mod2)

Intensity * Duration

big.mod3 <- lm(blastintensity.duration.t.w.s ~ condition_dum*KIMS.t.w.s + 
                 condition_dum*BSCS.t.w.s + condition_dum*BAQ.t.w.s + 
                 condition_dum*SOPT.t.w.s + condition_dum*IAT.t.w.s, 
               data = data, na.action="na.exclude")
check_model(big.mod3)

1st Intensity

big.mod4 <- lm(blastintensity.first.t.w.s ~ condition_dum*KIMS.t.w.s + 
                 condition_dum*BSCS.t.w.s + condition_dum*BAQ.t.w.s + 
                 condition_dum*SOPT.t.w.s + condition_dum*IAT.t.w.s, 
               data = data, na.action="na.exclude")
check_model(big.mod4)

1st Duration

big.mod5 <- lm(blastduration.first.t.w.s ~ condition_dum*KIMS.t.w.s + 
                 condition_dum*BSCS.t.w.s + condition_dum*BAQ.t.w.s + 
                 condition_dum*SOPT.t.w.s + condition_dum*IAT.t.w.s, 
               data = data, na.action="na.exclude")
check_model(big.mod5)

1st Intensity * Duration

big.mod6 <- lm(blastintensity.duration.first.t.w.s ~ condition_dum*KIMS.t.w.s + 
                 condition_dum*BSCS.t.w.s + condition_dum*BAQ.t.w.s + 
                 condition_dum*SOPT.t.w.s + condition_dum*IAT.t.w.s, 
               data = data, na.action="na.exclude")
check_model(big.mod6)

50 trials

big.mod7 <- lm(all50trials.t.w.s ~ condition_dum*KIMS.t.w.s + 
                 condition_dum*BSCS.t.w.s + condition_dum*BAQ.t.w.s + 
                 condition_dum*SOPT.t.w.s + condition_dum*IAT.t.w.s, 
               data = data, na.action="na.exclude")
check_model(big.mod7)

All the models assumptions look pretty good overall actually, even with all these variables. The lines for linearity and homoscedasticity are a bit skewed but nothing too crazy. Let’s now look at the results.

Moderations

Blast Intensity

big.mod1 %>% 
  nice_lm(b.label = "B") %>% 
  nice_table(highlight = TRUE)

Blast Duration

big.mod2 %>% 
  nice_lm(b.label = "B") %>% 
  nice_table(highlight = TRUE)

Intensity * Duration

big.mod3 %>% 
  nice_lm(b.label = "B") %>% 
  nice_table(highlight = TRUE)

1st Intensity

big.mod4 %>% 
  nice_lm(b.label = "B") %>% 
  nice_table(highlight = TRUE)

1st Duration

big.mod5 %>% 
  nice_lm(b.label = "B") %>% 
  nice_table(highlight = TRUE)

1st Intensity * Duration

big.mod6 %>% 
  nice_lm(b.label = "B") %>% 
  nice_table(highlight = TRUE)

All 50 trials

big.mod7 %>% 
  nice_lm(b.label = "B") %>% 
  nice_table(highlight = TRUE)

Interpretation: The condition by trait self-control (brief self-control scale, BSCS) interaction comes up for all variables (so it must be somewhat reliable).

Interaction plots

Let’s plot the main significant interaction(s).

Blast Intensity

interact_plot(big.mod1, pred = "condition_dum", modx = "BSCS.t.w.s", 
              modxvals = NULL, interval = TRUE, x.label = "Condition", 
              pred.labels = c("Control", "Mindfulness"),
              legend.main = "Trait Self-Control")

Blast Duration

interact_plot(big.mod2, pred = "condition_dum", modx = "BSCS.t.w.s", 
              modxvals = NULL, interval = TRUE, x.label = "Condition", 
              pred.labels = c("Control", "Mindfulness"),
              legend.main = "Trait Self-Control")

Intensity * Duration

interact_plot(big.mod3, pred = "condition_dum", modx = "BSCS.t.w.s", 
              modxvals = NULL, interval = TRUE, x.label = "Condition", 
              pred.labels = c("Control", "Mindfulness"),
              legend.main = "Trait Self-Control")

1st Intensity

interact_plot(big.mod4, pred = "condition_dum", modx = "BSCS.t.w.s", 
              modxvals = NULL, interval = TRUE, x.label = "Condition", 
              pred.labels = c("Control", "Mindfulness"),
              legend.main = "Trait Self-Control")

1st Duration

interact_plot(big.mod5, pred = "condition_dum", modx = "BSCS.t.w.s", 
              modxvals = NULL, interval = TRUE, x.label = "Condition", 
              pred.labels = c("Control", "Mindfulness"),
              legend.main = "Trait Self-Control")

1st Intensity * Duration

interact_plot(big.mod6, pred = "condition_dum", modx = "BSCS.t.w.s", 
              modxvals = NULL, x.label = "Condition", interval = TRUE, 
              pred.labels = c("Control", "Mindfulness"), 
              legend.main = "Trait Self-Control")

50 trials

interact_plot(big.mod7, pred = "condition_dum", modx = "BSCS.t.w.s", 
              modxvals = NULL, interval = TRUE, x.label = "Condition", 
              pred.labels = c("Control", "Mindfulness"),
              legend.main = "Trait Self-Control")

Interpretation: The interaction is pretty much the same for all models. Counterintuitively, for people with low self-control, the priming mindfulness condition relates to lower aggression relative to the control condition. In contrast, for people with high self-control, the priming mindfulness condition relates to higher aggression.

Simple slopes

Let’s look at the simple slopes now (only for the significant interaction).

Blast Intensity

big.mod1 %>%
  nice_lm_slopes(predictor = "condition_dum",
                 moderator = "BSCS.t.w.s") %>% 
  nice_table(highlight = TRUE)

Blast Duration

big.mod2 %>%
  nice_lm_slopes(predictor = "condition_dum",
                 moderator = "BSCS.t.w.s") %>% 
  nice_table(highlight = TRUE)

Intensity * Duration

big.mod3 %>%
  nice_lm_slopes(predictor = "condition_dum",
                 moderator = "BSCS.t.w.s") %>% 
  nice_table(highlight = TRUE)

1st Intensity

big.mod4 %>%
  nice_lm_slopes(predictor = "condition_dum",
                 moderator = "BSCS.t.w.s") %>% 
  nice_table(highlight = TRUE)

1st Duration

big.mod5 %>%
  nice_lm_slopes(predictor = "condition_dum",
                 moderator = "BSCS.t.w.s") %>% 
  nice_table(highlight = TRUE)

1st Intensity * Duration

big.mod6 %>%
  nice_lm_slopes(predictor = "condition_dum",
                 moderator = "BSCS.t.w.s") %>% 
  nice_table(highlight = TRUE)

All 50 trials

big.mod7 %>%
  nice_lm_slopes(predictor = "condition_dum",
                 moderator = "BSCS.t.w.s") %>% 
  nice_table(highlight = TRUE)

Interpretation: The effect of priming mindfulness on blast intensity is only significant for people with a high self-control.

Conclusions

Based on the results, it seems that the interaction of interest comes up for all six measures of blast aggression (intensity, duration, the combination of the two, and the first blast of each type), suggesting it is reliable.

The effect sizes are slightly lower for measures of first blast (sr2 = 0.2) than the average intensity or duration (sr2 = 0.35), or intensity * duration (sr2 = 0.4).

Therefore, based on the marginally larger effect size, perhaps it does make sense to use the intensity * duration combination in future studies. My intuition is also that the effect is more reliable for reactive aggression (all trials) than proactive aggression (first measure only). Another reason to avoid using only the first trials is that they lead to problems with the distributions (i.e., they are not normal and are difficult to transform to normality).

There is another reason why using the product of intensity and duration might make more theoretical sense. Technically speaking, if a participant sets the intensity to 10, but duration to 0, there is no actual sound blast for that trial. Similarly, if a participant sets the duration to 10, but intensity to 0, there is no actual sound blast for that trial. Taking the product of intensity and duration takes this dynamic into account. In contrast, other methods using the sum of intensity and duration, or yet again the average of all 50 trials (intensity and duration) does not. Taking the average of that trial with intensity = 10 and duration = 0 would yield 5, whereas it should be 0 because no sound was actually administered for that trial.

Preregistration

Recommandation

For the preregistration, I would suggest committing to using the average product of intensity and duration of all trials, and optimally transform it to normality via the bestNormalize package, as suggested above, and using the same design.

This strategy is similar to those who use the product of intensity with the log of duration, so the following papers could be cited (next tab).

Citable papers

Volume x Duration, average of all trials (25)

Arriaga, P., Monteiro, M. B., & Esteves, F. (2011). Effects of playing violent computer games on emotional desensitization and aggressive behavior. Journal of Applied Social Psychology, 41(8), 1900-1925. https://doi.org/10.1111/j.1559-1816.2011.00791.x

Participants’ ratings of the two indexes of noise (i.e., intensity, duration) that were administered to the opponent were multiplied to compute a global measure of aggressive behavior (see Bartholow et al., 2005).

Volume x Duration, multiplied averages of all trials (25)

Bartholow, B. D., Sestir, M. A., & Davis, E. B. (2005). Correlates and consequences of exposure to video game violence: Hostile personality, empathy, and aggressive behavior. Personality and Social Psychology Bulletin, 31(11), 1573-1586. https://doi.org/10.1177/0146167205277205

In this study, average noise intensity and duration settings were multiplied to form a composite aggressive behavior score.

Volume x log(Duration), average of all trials (25) / linear/quadratic contrasts across all trials (25)

Lindsay, J. J. & Anderson, C. A. (2000). From antecedent conditions to violent actions: A general affective aggression model. Personality and Social Psychology Bulletin, 26(5), 533-547. https://doi.org/10.1177/0146167200267002

The duration settings (hold times) were found to be positively skewed. We reduced this skew by subjecting the duration settings to a log transformation. For each participant, we multiplied the transformed duration setting by the intensity setting for each trial separately.

Volume x √Duration, average of all trials (25)

Carnagey, N. L. & Anderson, C. A. (2005). The effects of reward and punishment in violent video games on aggressive affect, cognition, and behavior. Psychological Science, 16(11), 882-889. https://doi.org/10.1111/j.1467-9280.2005.01632.x

An aggressive-energy score was calculated for each trial by taking the square root of the duration of noise chosen for the opponent and multiplying this value by the intensity of the noise chosen.

Last minute exploration

One question that arises is whether we should include any other variables other than the BSCS since this is the only variable of interest giving an interesting effect. When defining the sample size for the preregistration, we got an sr2 of the primary model (blast * intensity) of .04, which is kind of large for these effects. However, that is for the model that controls for many other variables and interactions. When only using BSCS in the model, the effect is smaller, .03, thus changing the required sample size for the power analysis.

However, even if we were to include those variables, perhaps we need not include them as interaction terms, but simply as covariates. Let’s test this below by redefining model 3 again with all other variables as covariates.

Edit: after some exploration, the most parsimonious model seems to be to control for KIMS, but not only for KIMS, but also for its interaction with the condition.

big.mod3 <- lm(blastintensity.duration.t.w.s ~ KIMS.t.w.s + 
                 condition_dum*KIMS.t.w.s +  
                 condition_dum*BSCS.t.w.s, 
               data = data, na.action="na.exclude")
big.mod3 %>% 
    nice_lm(b.label = "B") %>% 
    nice_table(highlight = TRUE)

Then we still get the sr2 = .04, without having to worry about administrating the SOPT, IAT, BAQ, etc.

So first study reports the large models with all variables, and the second study only the BSCS, along with the KIMS.

Package References

report::cite_packages(sessionInfo())

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• Long JA (2019). interactions: Comprehensive, User-Friendly Toolkit forProbing Interactions. R package version 1.1.0,https://cran.r-project.org/package=interactions.
• Lüdecke D, Ben-Shachar M, Patil I, Waggoner P, Makowski D (2021).”performance: An R Package for Assessment, Comparison and Testing ofStatistical Models.” Journal of Open Source Software, 6(60), 3139.doi:10.21105/joss.03139 https://doi.org/10.21105/joss.03139.
• Lüdecke D, Patil I, Ben-Shachar M, Wiernik B, Waggoner P, Makowski D(2021). “see: An R Package for Visualizing Statistical Models.”Journal of Open Source Software, 6(64), 3393.doi:10.21105/joss.03393 https://doi.org/10.21105/joss.03393.
• Makowski D, Ben-Shachar M, Patil I, Lüdecke D (2021). “AutomatedResults Reporting as a Practical Tool to Improve Reproducibility andMethodological Best Practices Adoption.” CRAN.https://github.com/easystats/report.
• Microsoft, Weston S (2022). foreach: Provides Foreach LoopingConstruct. R package version 1.5.2,https://CRAN.R-project.org/package=foreach.
• Peterson RA (2021). “Finding Optimal Normalizing Transformations viabestNormalize.” The R Journal, 13(1), 310-329.doi:10.32614/RJ-2021-041 https://doi.org/10.32614/RJ-2021-041.Peterson RA, Cavanaugh JE (2020). “Ordered quantile normalization: asemiparametric transformation built for the cross-validation era.”Journal of Applied Statistics, 47(13-15), 2312-2327.doi:10.1080/02664763.2019.1630372https://doi.org/10.1080/02664763.2019.1630372.
• R Core Team (2022). R: A Language and Environment for StatisticalComputing. R Foundation for Statistical Computing, Vienna, Austria.https://www.R-project.org/.
• Revelle W (2022). psych: Procedures for Psychological, Psychometric,and Personality Research. Northwestern University, Evanston,Illinois. R package version 2.2.5,https://CRAN.R-project.org/package=psych.
• Stekhoven DJ (2022). missForest: Nonparametric Missing ValueImputation using Random Forest. R package version 1.5.Stekhoven DJ, Buehlmann P (2012). “MissForest - non-parametric missingvalue imputation for mixed-type data.” Bioinformatics, 28(1),112-118.
• Thériault R (2022). rempsyc: Convenience Functions for Psychology. Rpackage version 0.0.9, https://rempsyc.remi-theriault.com.
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• Tierney N, Cook D, McBain M, Fay C (2021). naniar: Data Structures,Summaries, and Visualisations for Missing Data. R package version0.6.1, https://CRAN.R-project.org/package=naniar.
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